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Journal of Chemical Theory and Computation

Simulation of Condensed-Phase Spectroscopy with Near-Term Digital Quantum Computers

Chee‐Kong Lee, Chang‐Yu Hsieh, Shengyu Zhang, Liang Shi

Published Oct 14, 2021• 17 citations
Publisher

Abstract

Spectroscopy is an indispensable tool for understanding the structures and dynamics of molecular systems. However, computational modeling of spectroscopy is challenging due to the exponential scaling of computational complexity with system sizes unless drastic approximations are made. Quantum computers could potentially overcome these classically intractable computational tasks, but the existing approaches using quantum computers to simulate spectroscopy can only handle isolated and static molecules. In this work, we develop a workflow that combines multi-scale modeling and a time-dependent variational quantum algorithm to compute the linear spectroscopy of systems interacting with their condensed-phase environment via the relevant time correlation function. We demonstrate the feasibility of our approach by numerically simulating the UV-vis absorption spectra of organic semiconductors. We show that our dynamical approach captures several spectral features that are otherwise overlooked by static methods. Our method can be directly used for other linear condensed-phase spectroscopy and could potentially be extended to nonlinear multi-dimensional spectroscopy.

DOI
10.1021/acs.jctc.1c00849

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Spectroscopy is an indispensable tool for understanding the structures and dynamics of molecular systems. However, computational modeling of spectroscopy is challenging due to the exponential scaling of computational complexity with system sizes unless drastic approximations are made. Quantum computers could potentially overcome these classically intractable computational tasks, but the existing approaches using quantum computers to simulate spectroscopy can only handle isolated and static molecules. In this work, we develop a workflow that combines multi-scale modeling and a time-dependent variational quantum algorithm to compute the linear spectroscopy of systems interacting with their condensed-phase environment via the relevant time correlation function. We demonstrate the feasibility of our approach by numerically simulating the UV-vis absorption spectra of organic semiconductors. We show that our dynamical approach captures several spectral features that are otherwise overlooked by static methods. Our method can be directly used for other linear condensed-phase spectroscopy and could potentially be extended to nonlinear multi-dimensional spectroscopy.
Spectroscopy is an indispensable tool in understanding the structures and dynamics of molecular systems. However computational modelling of spectroscopy is challenging due to the exponential scaling of computational complexity with system sizes unless drastic approximations are made. Quantum computer could potentially overcome these classically intractable computational tasks, but existing approaches using quantum computers to simulate spectroscopy can only handle isolated and static molecules. In this work we develop a workflow that combines multi-scale modeling and time-dependent variational quantum algorithm to compute the linear spectroscopy of systems interacting with their condensed-phase environment via the relevant time correlation function. We demonstrate the feasibility of our approach by numerically simulating the UV-Vis absorption spectra of organic semiconductors. We show that our dynamical approach captures several spectral features that are otherwise overlooked by static methods. Our method can be directly used for other linear condensed-phase spectroscopy and could potentially be extended to nonlinear multi-dimensional spectroscopy.
Quantum computers have the potential to simulate chemical systems beyond the capability of classical computers. Recent developments in hybrid quantum-classical approaches enable the determinations of the ground or low energy states of molecular systems. Here, we extend near-term quantum simulations of chemistry to time-dependent processes by simulating energy transfer in organic semiconducting molecules. We developed a multiscale modeling workflow that combines conventional molecular dynamics and quantum chemistry simulations with hybrid variational quantum algorithm to compute the exciton dynamics in both the single excitation subspace (i.e., Frenkel Hamiltonian) and the full-Hilbert space (i.e., multiexciton) regimes. Our numerical examples demonstrate the feasibility of our approach, and simulations on IBM Q devices capture the qualitative behaviors of exciton dynamics, but with considerable errors. We present an error mitigation technique that combines experimental results from the variational and Trotter algorithms, and obtain significantly improved quantum dynamics. Our approach opens up new opportunities for modeling quantum dynamics in chemical, biological, and material systems with quantum computers.
Multidimensional optical spectroscopies are powerful techniques to investigate energy transfer pathways in natural and artificial systems. Because of the high information content of the spectra, numerical simulations of the optical response are of primary importance to assist the interpretation of spectral features. However, the increasing complexity of the investigated systems and their quantum dynamics call for the development of novel simulation strategies. In this work, we consider using digital quantum computers. By combining quantum dynamical simulation and nonlinear response theory, we present a quantum algorithm for computing the optical response of molecular systems. The quantum advantage stems from the efficient quantum simulation of the dynamics governed by the molecular Hamiltonian, and it is demonstrated by explicitly considering exciton-vibrational coupling. The protocol is tested on a near-term quantum device, providing the digital quantum simulation of the linear and nonlinear response of simple molecular models.
Spectroscopy is the most important method for probing the structure of molecules. However, predicting molecular spectra on classical computers is computationally expensive, with the most accurate methods having a cost that grows exponentially with molecule size. Quantum computers have been shown to simulate simple types of optical spectroscopy efficiently -- with a cost polynomial in molecule size -- using methods such as time-dependent simulations of photoinduced wavepackets. Here, we show that any type of spectroscopy can be efficiently simulated on a quantum computer using a time-domain approach, including spectroscopies of any order, any frequency range, and involving both electric and magnetic transitions. Our method works by computing any spectroscopic correlation function based on the corresponding double-sided Feynman diagram, the canonical description of spectroscopic interactions. The approach can be used to simulate spectroscopy of both closed and open molecular systems using both digital and analog quantum computers.
Modern computational techniques used to simulate quantum chemistry are on the boundary of tractability due to the exponential growth of the molecular wavefunction, requiring a careful balance between molecule size and simulation accuracy. In recent years, quantum computing has risen in popularity as a potential alternative to conventional (classical) techniques; however, most methods rely on access to "digital" quantum computers composed of qubits and quantum gates, which at present are severely limited by noise. We have developed a real-time, analog approach to simulate vibronic chemical dynamics with existing quantum technology. Our approach uses an intuitive mapping of molecular electronic and vibrational degrees of freedom onto quantum resonators and qudit (d-level system) states, with controllable couplings between degrees of freedom. The measurement output can be mapped onto different time-dependent observables, including the time-domain simulation of vibronic spectra. Our approach can also incorporate controlled sources of noise to simulate system-bath interactions and dissipative dynamics at a minimal cost. We present experimental results using a trapped-ion device, thus showing the potential for near-term simulation of chemical dynamics in complex environments beyond the abilities of classical computers.
Nonlinear spectroscopy is a cornerstone of quantum science, providing unique access to multi-point correlations, quantum coherence, and couplings that are invisible to linear methods. However, classical simulation of these phenomena is fundamentally limited by the exponential growth of the Hilbert space, and practical quantum algorithms for the nonlinear regime have remained largely unexplored. Here, we present a unified quantum algorithmic framework for computing nnn-th order nonlinear spectroscopies. By reformulating multi-time responses as a weighted sum of expectation values at finite pump amplitudes via a generalized parameter shift rule, our approach bypasses the costly evaluation of high-order commutators and time-dependent operator expansions. This reformulation enables efficient execution via real-time evolution on current quantum hardware, ensuring inherent noise resilience. We validate the framework on IBM's superconducting quantum processors, successfully obtain higher-order response functions of a 12-qubit XXZ spin-chain. Furthermore, the versatility of our method is demonstrated by resolving quasi-particle excitation spectra in spin-liquids and identifying interaction-induced cross-peaks in atomic systems. Our results establish a practical and scalable pathway for probing complex quantum dynamics on near-term quantum devices, extending the reach of quantum simulation into the nonlinear domain.